Singular Value Decomposition

Dive deep into the Singular Value Decomposition (SVD) algorithm through this comprehensive 7-hour lecture series based on Chapter 1 of "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz. Explore SVD's mathematical foundations, matrix approximation techniques, and applications in image compression, matrix completion, and the Netflix Prize. Learn about unitary transformations, linear systems of equations, least squares regression, and the pseudoinverse. Discover Principal Component Analysis (PCA) and its implementation in MATLAB and Python. Investigate eigenfaces, optimal truncation, and the importance of alignment in SVD. Conclude with an examination of randomized SVD techniques, including power iterations and oversampling, with practical code examples in both MATLAB and Python.

Singular Value Decomposition (SVD): Overview.
Singular Value Decomposition (SVD): Mathematical Overview.
Singular Value Decomposition (SVD): Matrix Approximation.
Singular Value Decomposition (SVD): Dominant Correlations.
SVD: Image Compression [Matlab].
SVD: Image Compression [Python].
The Frobenius Norm for Matrices.
SVD Method of Snapshots.
Matrix Completion and the Netflix Prize.
Unitary Transformations.
Unitary Transformations and the SVD [Matlab].
Unitary Transformations and the SVD [Python].
Linear Systems of Equations, Least Squares Regression, Pseudoinverse.
Least Squares Regression and the SVD.
Linear Systems of Equations.
Linear Regression.
Linear Regression 1 [Matlab].
Linear Regression 2 [Matlab].
Linear Regression 1 [Python].
Linear Regression 2 [Python].
Linear Regression 3 [Python].
Principal Component Analysis (PCA).
Principal Component Analysis (PCA) [Matlab].
Principal Component Analysis (PCA) 1 [Python].
Principal Component Analysis (PCA) 2 [Python].
SVD: Eigenfaces 1 [Matlab].
SVD: Eigenfaces 2 [Matlab].
SVD: Eigenfaces 3 [Matlab].
SVD: Eigenfaces 4 [Matlab].
SVD: Eigen Action Heros [Matlab].
SVD: Eigenfaces 1 [Python].
SVD: Eigenfaces 2 [Python].
SVD: Eigenfaces 3 [Python].
SVD and Optimal Truncation.
SVD: Optimal Truncation [Matlab].
SVD: Optimal Truncation [Python].
SVD and Alignment: A Cautionary Tale.
SVD: Importance of Alignment [Python].
SVD: Importance of Alignment [Matlab].
Randomized Singular Value Decomposition (SVD).
Randomized SVD: Power Iterations and Oversampling.
Randomized SVD Code [Matlab].
Randomized SVD Code [Python].